FIG. 1 shows a schematic view of imaging of a 2D optical lens.
A general 2D optical lens is formed by a spherical lens 1. After an object point o of a paraxial point light source goes through a 2D optical lens 1, a characteristic of the image includes a point-shaped image point ixy, and the relation of its image position follows the principle of geometric optics as shown in Equation (1) as listed below.
                                          1                          l              o                                +                      1                          l              i                                      =                  1          f                                    (        1        )            where, lo is an object distance of the point light source o, and li is an image distance, and f is a focal length of the optical lens 1. In addition, another characteristic of the geometric optical image resides on that a non-deviated light exists between the point light source o and the image point ixy, and the light passes through a geometric center Olens of the 2D optical lens 1.
FIG. 2 is a schematic view of forming an image by a 1D optical lens.
A general 1D optical lens is formed by semi-cylindrical lenses 2, 3, and its imaging principle follows the theory of geometric optics, but the 1D optical lens has the 1D imaging ability only. Therefore, 1D longitudinal focusing optical lens 2 transforms a point light source into a transverse line image iy, and a 1D transverse focusing optical lens 3 transforms a point light source into a longitudinal line image ix, and the image transformation also follows the principle of geometric optics as listed in Equation (1).
FIG. 3 is a schematic view of a general optical camera. The camera 5 can be a general optical camera, a digital camera, or a camcorder, comprising an adjustable aperture 6, a variable focusing lens module 7, an image sensing and recording device 8. For the object point o1, an appropriate adjustment of the focal length f of the variable focusing lens module 7 is made to obtain an image point i1, and form an image on the image recording device 8. In general, a relation of li≈f can be obtained due to the object distance l0 being larger than the focal length f.
For an object point o2 at a different distance, the variable focusing lens module 7 is used for obtaining another image point i2. By an appropriate adjustment of the size of the adjustable aperture 6, another similar image point i2 can be obtained on the image recording device 8.
FIG. 4(a) is a schematic view of a structure of a human eyeball.
Human eyeball 10 is similar to an optical camera, and mainly comprises an iris 11, an eye crystalline lens 13 and a retina 15. Compared with the optical camera, the function of the iris 11 is to adjust the size of the pupil 12 and can be considered as an adjustable aperture; the eye crystalline lens 13 serves as a lens, such that the ciliaris muscle 14 can be moved to change the curvature (or focal length) of the eye crystalline lens 13, and thus can be considered as a variable focusing lens; and the retina 15 can be considered as an image sensor for transmitting an obtained image to a brain through the optic nerve 16, and the brain processes, stores and recognizes the visual space. In general, the viewing direction of the eyeball 10 (or known as the visual axis 17, which is the optical axis of the optical system of the eyeball) bases on the up-and-down and left-and-right movements of the eyeball 10 to change the direction of the visual axis 17 in a limited extent. Further, the left-and-right and up-and-down rotation of the neck can change the direction of the visual axis 17 is a great extent.
FIG. 4(b) is a schematic view of a structure of a visual space.
As to the left and right eyes 21, 22, the visual space refers to the space existed and observed by the left and right eyes 21, 22. Firstly, a world coordinate system O(X, Y, Z) is defined, such that î, ĵ, {circumflex over (k)} are unit vectors of the coordinate axes in the coordinate system. The coordinate axes of the world coordinate system are fixed, and the world coordinate system constitutes the space to define the visual space. Further, another rotating but immoving neck coordinate system ON(XN, YN, ZN) is set at the origin (0, 0, 0) of the world coordinate system O(X, Y, Z) and îN, ĵN, {circumflex over (k)}N are set to be the unit vectors of the coordinate axes in the coordinate system, and the coordinate system ON(XN, YN, ZN) is rotated such that the axis ZN can be rotated to an angle Θ with respect to the axis YN, and the axis XN can be rotated to an angle Φ as shown in FIG. 4(c).
Further, a rotating but immoving left eye coordinate system OL(XL, YL, ZL) is set at the position (S/2, H, 0) of the neck coordinate system ON(XN, YN, ZN), and ûLX, ûLY, ûLZ are set to be the unit vectors of the coordinate axes, and a rotating but immoving right eye coordinate system OR(XR, YR, ZR) is set at the position (−S/2, H, 0) of ON(XN, YN, ZN), and ûRX, ûRY, ûRZ are set to be the unit vectors of the coordinate axes. Therefore ON(XN, YN, ZN) can be rotated to an angle of Θ or Φ to drive the rotation of OL(XL, YL, ZL), OR(XR, YR, ZR) and the point OH respectively, and Θ and Φ can be considered as angles of left-and-right (horizontal) and up-and-down (vertical) rotations of the neck. S is defined as the stereo base; OH is defined as the center of stereo base; and the length of H is considered as the height of cervical (neck) spine as shown in FIGS. 4(f) and 4(g).
In FIG. 4(b), a point FL at the position (0, 0, f) on the left eye coordinate system OL(XL, YL, ZL) is defined as the center position of the left eye crystalline lens. The axis ZL of the coordinate system OL(XL, YL, ZL) can be rotated to an angle θL with respect to the axis YL, and an angle φL with respect to the axis XL as shown in FIG. 4(d). Therefore, the angles θL, φL can be considered as the angles of left-and-right (horizontal) and up-and-down (vertical) rotations similar to the rotations of the left eyeball as shown in FIG. 4(f) and FIG. 4(g) respectively. Since the OL(XL, YL, ZL) of the left eye coordinate system is set on the retina, therefore the retina disposed proximate to the origin of the coordinates can be considered to be disposed on the plane XL-YL, and the plane XL-YL is defined as the plane of the left image.
In FIG. 4(b), a point FR at the position (0, 0, f) on the right eye coordinate system OR(XR, YR, ZR) is defined as of the center position of the right eye crystalline lens. The axis ZR of the coordinate system OR(XR, YR, ZR) can be rotated to an angle θR with respect to the axis YR, and an angle of φR with respect to the axis the axis XR as shown in FIG. 4(e). Therefore, the angles θR, φR can be considered as the angles of the rotations similar to left-and-right (horizontal) and up-and-down (vertical) rotations of the right eyeball as shown in FIGS. 4(f) and 4(g). Since the right eye coordinate system OR(XR, YR, ZR) is set on the retina therefore the retina disposed on the origin of the coordinates can be considered to be disposed on the plane XR-YR, and thus the plan XR-YR is defined as the plant of the right image.
FIG. 4(h) is a schematic geometric view of a (convergent point), an object point and each coordinate when two eyes are staring at a point. If two eyes are staring at a point in the front, the visual axes of two eyes are intersected at a point which is called a point of view or convergent point V. In other words, the axes ZL, ZR are the visual axes of the left and right eyes 21, 22 respectively, and the two visual axes must be intersected at a point which is the convergent point V. In a world coordinate system O(X, Y, Z), the coordinates of the convergent point V are (XV, YV, ZV). In the neighborhood of the convergent point V, there is an object point P, and in the world coordinate system O(X, Y, Z), the coordinates of the object point P are (XP, YP, ZP). Further, the position of a point image IL of the object point P formed by the left eye crystalline lens at the coordinate system of the left eye retina OL(XL, YL, ZL) are IL(xL, yL, 0); and the position of a point image IR of the object point P formed by the right eye crystalline lens at the OR(XR, YR, ZR) coordinate system of the right eye retina are IR(xR, yR, 0). In general, the angles (θL, θR, φL, φR, Θ, Φ) of the visual axes of both left and right eyes are adjusted appropriately to superimpose the convergent point V with the object point P to achieve the purpose of tracking and staring at an object.
As to human eyes, the up-and-down movements of the left and right eyeballs are limited to the same angle due to the evolution of human vision to recognize the 3D space effectively. In other words, φL=φR=φ. The condition of this limitation gives rise to a very important result which illustrates the vertical coordinate of point image IL, IR on the retina is consistent. In other words, yL=yR. Another necessary condition of causing such result is that the focal length of both left and right eyes must be equal to assure the consistency of the size of an image formed at the left and right eyes. The so-called parallax phenomenon refers to the difference between both images of an object point P, other than the convergent point V, formed on the retinas of the left and right eyes. In other words, xL≠xR. With the parallax, a human eye is capable of recognizing the distance of the space. Further, the value of a stereo base S is the most fundamental factor of determining the magnitude of the parallax. For the recognition of an object at a farther end, the parallax effect can be improved by increasing the stereo base S. As to the space recognition of a human vision, the angles (θL, θR, φ, Θ, Φ, S, f) are defined as a group of convergent parameters, and the parameters determine the parallax effect to achieve the purpose of recognizing the space.